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Gene X encodes a repressor that represses gene Y, which also encodes a repressor. Both X...

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Biology

Gene X encodes a repressor that represses gene Y, which alsoencodes a repressor. Both X and Y negatively regulate their ownpromoters. (a) At time t=0, X begins to be produced at rate β,starting from an initial concentration of X=0. What are thedynamics of X and Y? What are the response times of X and Y? Assumelogic input functions, with repression thresholds Kxx, Kxy for theaction of X on its own promoter and on the Y promoter and Kyy forthe action of Y on its own promoter. (b) At time t=0, production ofX stops after a long period of production, and X concentrationdecays from an initial steady-state level. What are the dynamics ofX and Y? What are the response times of X and Y?

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Ans a Assuming logic input function in all parameters dX dt x X Kxx X dY dt x X Kxy Y Kyy Y The concentration of X initially follows a familiar exponential rise as    See Answer
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